Using a linear function, it is found that the costs are given as follows:
With 6 rides: $24.With r rides: C(r) = 20 + 4r.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Considering the price of admission and the price per ride, the y-intercept is of 20 and the slope is of 4, the cost for r rides is given by:
C(r) = 20 + 4r.
Hence, for 6 rides, the cost is given by:
C(6) = 20 + 4 x 6 = $44.
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can someone please help mee(20 points and i will give brainliest!!!)
The vertex is the lowest/highest point, depending on if the parabola opens upwards or downwards.
So because the vertex opens upwards, we are looking for the lowest point which is at (2,-3).
Which expressions are equivalent to 8(-10x+3.5y-7)? Select two options.
A. -80x + 24.5y - 56
B. -80x + 28y - 56
C. 80x + 28y + 56
D. 4 (-20x + 7y - 14)
E. -4 (-20x + 7y - 14)
Answer:
B, D
Explanation:
8(-10x+3.5y-7)
= -80x + 28y - 56
4 (-20x + 7y - 14)
= 8(-10x+3.5y-7)
= -80x + 28y - 56
Answer:
B) -80x + 28y - 56
D) 4 (-20x + 7y - 14)
Original Expression:
⇒ 8(-10x+3.5y-7)
⇒ -80x + 28y - 56
Now confirmed that option B is correct when the expression is simplified which makes option A and C not applicable.
For option D:
⇒ 4 (-20x + 7y - 14)
⇒ -80x + 28y - 56
Option E is not correct as:
⇒ -4 (-20x + 7y - 14)
⇒ 80x - 28y + 56
For an each situation, it begin with the square field, measuring X centimetres by X centimetres. The dimensions of this square are to be changed. How do you write an expression for the area of the new square field, and then expand, and simplify? :/
A). The length of a side is being increased by 8 cm.
B). The length is being increased by 12 cm and the width is being decreased by 7 cm.
#A
New side
X+8Area
(x+8)²x²+16x+64 cm²#2
Now it has turned rectangle
Sides
x+12 and x-7
Area
(x+12)(x-7)Answer:
A) (x + 8)² cm² = (x² + 16x + 64) cm²
B) (x + 12)(x + 7) cm² = (x² + 19x + 84) cm²
Step-by-step explanation:
Formula
Area of a square = s² (where s is the side length)
Given side length of square field:
x cm⇒ Area of field = x² cm²
Part A
If the side length of the square field is increased by 8 cm then:
⇒ new side length = (x + 8) cm
Substitute the new side length into the formula for the area of a square:
⇒ Area of field = (x + 8)² cm²
Expand and simplify:
⇒ Area = (x + 8)²
⇒ Area = (x + 8)(x + 8)
⇒ Area = x(x + 8) + 8(x + 8)
⇒ Area = x² + 8x + 8x + 64
⇒ Area = (x² + 16x + 64) cm²
Part B
If the side length of the square field is increased by 12 cm and the width is decreased by 7 cm then:
⇒ new side length a = (x + 12) cm
⇒ new side length b = (x - 7) cm
Substitute the side lengths into the formula for area of a square:
⇒ Area of a square = s × s
⇒ Area of a square = a × b
⇒ Area of the field = (x + 12)(x + 7) cm²
Expand and simplify:
⇒ Area = (x + 12)(x + 7)
⇒ Area = x(x + 7) + 12(x + 7)
⇒ Area = x² + 7x + 12x + 84
⇒ Area = (x² + 19x + 84) cm²
Find the inverse of the radical function.
Enter the correct answer in the box.
The inverse of the given function is y = x³ + 2
Finding inverse of a radical functionGiven the radical function below expressed as;
f(x) = ∛x-2
This can be written as;
y = ∛x-2
Replace y with x
x = ∛y-2
Take the cube of both sides
x³ =y - 2
y = x³ + 2
Hence the inverse of the given function is y = x³ + 2
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Answer:
[tex]f^{-1} (x)=x^{3} +2[/tex]
Step-by-step explanation:
from plato
Determine the period.
two number cubes are rolled. Deterimine the number of ways that you could get a sum that is less than 5. The number cube is out of 6
Answer: six ways
Step-by-step explanation: The pairs when the cube is rolled that are less than five would be; (1,1), (1,2), (1,3), (2,1), (2,2), (3,1) since each cube is out of six.
Lola needs to sign 96 invitations. Using a stopwatch that measures time to tenths of a second, it takes Lola 5.3 seconds to sign her full name. Going by the accuracy of the stopwatch, which is the most accurate determination for the number of seconds Lola needs to sign all 96 invitations?
The time needed by Lola to sign all the 96 invitations is 508.8 second
What is a Product ?Product is the number obtained when two numbers are multiplied with each other
It is given that
Total Invitations that Lola needs to sign = 96
Time taken to sign full name = 5.3 seconds
Total time needed by Lola to sign invitations is
96 * 5.3
= 508.8 seconds
Therefore the time needed by Lola to sign all the 96 invitations is 508.8 second
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-1 1/3 - 1 2/3
answer in simplest form
Answer:
-3
Step-by-step explanation:
both are negatives, so think of it as addition
at the very end make sure you add the negative symbol :)
-1 1/3 - 1 2/3
The average hourly salary of workers in a warehouse is $14.50 with a standard deviation of $1.75. the shaded area of which curve represents the probability of the hourly salary being between $11 and $16.25?
Answer:
where is the question Skidoo
this is just a statement
Here are three studies:
a: june asks eight of her friends if they plan on buying a school lunch that day.
b: sam selects a random sample of coins from his coin bank to see how many of them are older than 1982.
c: peyton randomly selects six eggs from a carton. she randomly assigns three of them to be boiled for 10 minutes and the other three are boiled for 15 minutes. after they have cooled she compares how easy they are to peel.
for which of these studies can we draw conclusions of cause and effect?
a
b
c
none of them
Answer:
The answer is C
Step-by-step explanation:
Just got it.
Given: ΔABC
Prove: m∠ZAB = m∠ACB + m∠CBA
Triangle A C B is shown with its exterior angles. Line A B extends through point X. Line A C extends through point Y. Line C A extends through point X.
We start with triangle ABC and see that angle ZAB is an exterior angle created by the extension of side AC. Angles ZAB and CAB are a linear pair by definition.
We know that m∠ZAB + m∠CAB = 180° by the
.
We also know m∠CAB + m∠ACB + m∠CBA = 180° because
.
Using substitution, we have m∠ZAB + m∠CAB = m∠CAB + m∠ACB + m∠CBA.
Therefore, we conclude m∠ZAB = m∠ACB + m∠CBA using the
.
m∠ZAB + m∠CAB = 180° by the angle addition postulate
m∠CAB + m∠ACB + m∠CBA = 180° because of the triangle angle sum theorem
m∠ZAB = m∠ACB + m∠CBA using the subtraction property
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
m∠ZAB + m∠CAB = 180° by the angle addition postulate
m∠CAB + m∠ACB + m∠CBA = 180° because of the triangle angle sum theorem
m∠ZAB = m∠ACB + m∠CBA using the subtraction property
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Answer:
We start with triangle ABC and see that angle ZAB is an exterior angle created by the extension of side AC. Angles ZAB and CAB are a linear pair by definition.
We know that m∠ZAB + m∠CAB = 180° by the
✔ angle addition postulate
.
We also know m∠CAB + m∠ACB + m∠CBA = 180° because
✔ of the triangle angle sum theorem
.
Using substitution, we have m∠ZAB + m∠CAB = m∠CAB + m∠ACB + m∠CBA.
Therefore, we conclude m∠ZAB = m∠ACB + m∠CBA using the
✔ subtraction property
.
Step-by-step explanation:
If you vertically stretch the cubic parent function, f(x) = x3, what is the
equation of the new function?
Helen wants to have cake for her party. She needs 1 cake for every 8 people. Which expression helps her decide how many cakes to buy if p represents the number of people?
A. 8p
B. 1/8p
C. 8 + p
D. p-8
What is the midpoint of the segment (-6.-9)(16.5)
Answer:
M=(11,−2)
Step-by-step explanation:
Find the midpoint for [tex]P = \left(6, -9\right)P=(6,-9) \text{and} Q = \left(16, 5\right)Q=(16,5).[/tex]
The midpoint for two points P and Q is a point M whose coordinates is the half-sum of the corresponding coordinates of the two points.
Thus, [tex]M = \left(\frac{6 + 16}{2}, \frac{-9 + 5}{2}\right) = \left(11, -2\right)[/tex]
M=(11,−2)
Using the relationships between
perpendicular lines and their slopes, explain
why horizontal and vertical lines will always
be perpendicular.
Be sure to include the slopes of horizontal
and vertical lines as part of your answer
Answer:
They will always intersect at one point
Step-by-step explanation:
^^
(y ^ 4 * y ^ n)/(y ^ 2) = y ^ - 3 Find the value of n. (2 marks)
Answer:
n = -5
Step-by-step explanation:
Given:
[tex]\dfrac{y^4 \cdot y^n}{y^2}=y^{-3}[/tex]
Multiply both sides by y²:
[tex]\implies \dfrac{y^4 \cdot y^n}{\diagup \!\!\!\!\!y^2} \cdot \diagup \!\!\!\!\!y^2=y^{-3}\cdot y^2[/tex]
[tex]\implies y^4 \cdot y^n=y^{-3} \cdot y^2[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies y^{4+n}=y^{-3+2}[/tex]
[tex]\implies y^{4+n}=y^{-1}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]
[tex]\implies 4+n=-1[/tex]
Solve for n by subtracting 4 from both sides:
[tex]\implies 4+n-4=-1-4[/tex]
[tex]\implies n=-5[/tex]
Answer:
n = - 5
===========
Given equation:
[tex]\dfrac{y^4*y^n}{y^2} =y^{-3}[/tex]Solve it for n:
[tex]y^{4+n-2}=y^{-3}[/tex] [tex]y^{2+n}=y^{-3}[/tex][tex]2+n=-3[/tex][tex]n=-3-2[/tex][tex]n=-5[/tex]===========
Used properties:
[tex]a^b*a^c=a^{b+c}[/tex] product of exponents with same base[tex]a^b/a^c=a^{b-c}[/tex] division of exponents with same baseIf [tex]a^b=a^c[/tex] then [tex]b = c[/tex] equal exponents with same baseGiven the expression 3(4²) + 4 + 16-9, which operation would you perform first?
A. 3x4
B. 4²
C. 4+ 16
D.
16-9
Answer: 4²
Step-by-step explanation:
There is some rule but just remember:
1. parenthesis
2. exponents
3. division/multiplication
4. subtraction/addition
Drag the fractions to put them in order from least to greatest. 1/2 1/3 1/6 4/9
Answer:
See below
Step-by-step explanation:
If you can't tell just by looking at them, you will need to convert them all to fractions of a common denominator .....in this case (the smallest) common denominator would be 18
1/2 = 9/18
1/3 = 6/18
1/6 = 3/18
4/9 = 8/ 18 so now you can see least to greatest is
1/6 1/3 1/2 4/9
Answer:
To make it best for you, you can find The Lowest common denominator between the fractions by then you can be able to decide which ones is small to biggest.LCD is 18 therfore respectively we have 9[tex] \frac{9}{18} ... \frac{6}{18} ... \frac{3}{18} ... \frac{8}{12} .... \\ therfore \: \frac{1}{6} ... \frac{1}{3} ... \frac{4}{9} .... \frac{1}{2} ...[/tex]8. A group of teenagers were surveyed to find out whether they like to drink coffee or tea. The result is shown below. •21 teenagers like to drink coffee or tea •3 teenagers like to drink coffee and tea. •2 teenagers do not like to drink coffee or tea. Based on the information, calculate (a) the total number of teenagers in the group. (b) the number of teenagers who like to drink coffee only or tea only.
a) 26 teenagers are in the group. 21+3+2=26
b) 21 like to drink coffee or tea only. (3 like both and 2 like neither, so 21 enjoy one or the other)
The midpoint of AB is M(-2, -1) If the coordinates of AA are (-7, 2) what are the coordinates of B?
Answer:
(3,-4)
Step-by-step explanation:
Tawny wrote an expression to represent “the quotient of 82 and a number, decreased by 26.” She then evaluated the expression when n = 2. Which statements are true about the expression and its value? Check all that apply.
The correct expression is 82 minus StartFraction 24 Over n EndFraction.
To evaluate the expression, subtract 26 from the quotient.
To evaluate the expression, subtract the quotient from 82.
The correct expression is StartFraction 82 Over n EndFraction minus 26.
The operations include division and subtraction.
To evaluate, substitute 24 for the variable in the equation.
The value of the expression is 15.
The value of the expression (82/n – 26) at n = 2 will be 15. Then the correct options are B, D, E, and G.
What is division?Division means the separation of something into different parts, sharing of something among different people, places, etc.
Tawny wrote an expression to represent “the quotient of 82 and a number, decreased by 26.”
She then evaluated the expression when n = 2.
Then the expression will be
⇒ 82 / n – 26
If the value of n is 2, then the value of the expression will be
⇒ 82 / 2 – 26
⇒ 41 – 26
⇒ 15
Then the correct options are B, D, E, and G.
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Lila and mick have pets. lila's pet has 6.73 toy bones. mick's pet has 5 times the many toy bones lila has. how many bones does mick's pet have?
Answer:33.65
Step-by-step explanation:
6.73 x 5= 33.65
The marketing manager of a cell-phone company wants to determine which cell phone model most of her customers prefer. She separates a list of her customers into three age groups and then randomly selects a sample from each group proportional to the number of customers in each group.
What sampling method did she use?
A. Simple random sampling
B. Stratified random sampling
C. Systematic random sampling
D. Non-random sampling
Answer:
C
Step-by-step explanation:
I guess it is the answer because the manager separates the customers into 3 ange groups and randomly selects a sample from each group
Answer:
B. Stratified random sampling
Step-by-step explanation:
i need a little help please i am so bad with exponents right now -
Answer:
the answer is -1/8
Step-by-step explanation:
The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5cm². calculate correct to 3 Significant figures, the base radius, r ,height h Volume of the cone [take π 22/7]
The volume of the cone is V = 381.15 cu.cm
What is the Curved Surface Area of the cone ?The curved surface area of the cone is given by
A = πrl
The slant height given in the question is
l = 10.5 cm
A = 115.5 sq.cm
radius = ?
Height = ?
Volume = ?
Using the Curved Surface Area Formula
115.5 = π * r * 10.5
taking π = 22/7
r = 3.5 cm
The slant height is given by
[tex]\rm l = \sqrt{ r^2 + h^2}[/tex]
Therefore the height is
[tex]\rm h = \sqrt{ 10.5^2 -3.5^2}[/tex]
h = 9.9 cm
The volume of the cone is
V = π r²h
V = (22/7) * 3.5 * 3.5 * 9.9
V = 381.15 cu.cm
The volume of the cone is V = 381.15 cu.cm
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What is the value of x?
to
x = [? ]°
36°
Enter
I will give you 25 pts
The vale of x is 54°.
What is tangent?The tangent is defined as a line touching circles or an ellipse at only one point.
We have,
As, the tangent is perpendicular to the radius of the circle.
So, using Angle sum property in a triangle
x+90+36= 180
x+126 = 180
x= 54°
Hence, the value of x is 54°
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I’m having trouble understanding how to solve this someone please help ASAP thank you!
Use the Law of Cosines to solve the problem. You must solve for BC first. Solve this problem in order.
A ship travels due west for 94 miles. It then travels in a northwest direction for 119 miles and ends up 173 miles from its original position. To the nearest tenth of a degree, how many degrees north of west (x) did it
turn when it changed direction? Show your work.
i need help asapppppp
Answer:
a
Step-by-step explanation:
2^3 = 8; 4^3 = 64; 8/64 = 1/8
(g^5)^3 = g^15
(h^2)^3 = h^6
g^15/8h^6
Calculate the middle number in the middle of 12.7 and 21.2.
The middle number is 16.95
What is Number system?The collection of numbers is called the number system. These numbers are of different types such as natural numbers, whole numbers, integers, rational numbers and irrational numbers.
Given:
Numbers are 12.7 and 21.2
Difference between number
= 21.2-12.7
=8.5
middle number
= 12.7+ 8.5/2
= 12.7+ 4.25
= 16.95
Hence, the middle number is 16.95.
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find the positive square root of 217.05 and 100.2001......with division method
The square root of 217.05 is 14.73 and the square root of 100.2001 is 10.01.
How to depict the square root?It should be noted that square root is factor of a number that when multiplied by itself will give the original number.
In this case, the square root of 217.05 is 14.73 and the square root of 100.2001 is 10.01.
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